WASHINGTON — Forget the federal court cases challenging the new health-care law — four Senate Democrats are already looking for ways to kill a key funding provision at the heart of the program.

The provision — a fine that certain people who fail to buy a health-insurance plan will have to pay — is central to lawsuits challenging the law’s constitutionality that are on track to reach the Supreme Court.

One Democratic senator, Ben Nelson of Nebraska, is looking to draft legislation within weeks to replace the mandate, though it is considered essential to the way the law is structured.

Sen. Claire McCaskill (D-Mo.), an ally of President Obama, is also looking to get behind an alternative.